{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 什么是多项式回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1, 1)\n",
    "# 二次函数生成y\n",
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 线性回归？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "y_predict = lin_reg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_predict, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.5880636780290829"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "lin_reg.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 解决方案， 添加一个特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X2 = np.hstack([X, X**2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 2)"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "# 相当于根据原有数据集创建新的数据集\n",
    "# 每一个样本中有两个特征\n",
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lin_reg2 = LinearRegression()\n",
    "lin_reg2.fit(X2, y)\n",
    "y_predict2 = lin_reg2.predict(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "# 因为x是没有顺序的，如果生成折线图的话需要进行排序\n",
    "# 对应的y也要进行排列\n",
    "plt.plot(np.sort(x), y_predict2[np.argsort(x)], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.02693038, 0.41565944])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "lin_reg2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2.235582424116836"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "lin_reg2.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.8076662426347568"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "lin_reg2.score(X2, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.8 64-bit ('anaconda': conda)",
   "language": "python",
   "name": "python36864bitanacondaconda085db2e8b14649f4b32196068f7124e9"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}